(552) 
as deduced from the micrometer readings on the marks, we have deduced 
the approximate values of the azimuth of the transit circle from 
those of the azimuths of the marks. 
The personal equations of the observers which have been applied 
here are the differences of the Right Ascension of Polaris according 
to their observations and the Right Ascension of this star according 
to the “Fundamental Catalog der Astronomische Gesellschaft.” 'These 
approximate values are deduced from former observations of Polaris, 
in the supposition that the personal equation for both culminations 
and under all circumstances is the same. 
6. After the reduction mentioned in § 5 each time of transit o 
should represent, if the elements of reduction were exact, the 
apparent Right Ascension of Polaris ¢ as deduced for the moment 
of observation from the mean place of the Fundamental Catalog. 
The apparent Right Ascensions are borrowed from the “Berliner 
Jahrbuch” ; only in the years 1882—85 the mean Right Ascension 
of the “Jahrbuch” differs from that of the “Katolog” and then the 
apparent Right Ascension of the Jahrbuch have been reduced to 
the later system. The differences o—e of the observed and com- 
puted Right Ascensions further have served to determine the cor- 
rections of the personal equation and the instrumental errors and 
principally those of the assumed azimuths of the marks. 
7. For the discussion of the quantities o—c the following course has 
been taken. First the mean of the values o—c for three successive months 
have been formed for each observer and for each culmination separately in 
order to determine that part of the values o—e which, independently 
of the influence of the accidental and systematical errors of the 
instrument, is the same for the two culminations. For the deter- 
mination of this part the observations of the two observers at first 
have been treated separately. In so far as the two culminations were 
both observed during the same periods of three months half the 
sums of their mean results are taken; as it appeared that these values 
showed periodical annual variations, the periodic part has first been 
deduced and afterwards the annual means of the residuals are com- 
puted. It then appeared that the results for the two observers 
agreed fairly well, both with regard to the annual means and to 
the co-efficients of the periodic part. Therefore J have combined 
the corresponding results of the two observers in one system; and 
have represented graphically the annual means obtained in this way 
by a smooth curve. The sum of the ordinates of this curve and of 
the deviations resulting from the periodical annual variation form 
the part of the quantities o—c, common to both the culminations; 
